Download Astr 250 Notes on the Bohr Model Classical model

Astr 250
Notes on the Bohr Model
Classical model - centripetal force provided by the Coulomb attractive force to keep an electron in a
circular orbit about a nucleus (see figure below)
- problem is that electron radiate when accelerated, thus should be losing energy in
circular orbits, thus atoms would be collapsing.
Bohr model
- assumed only certain orbits are allowed, and those do not radiate.
- that these allowed orbits have discrete angular momentum, L = n h / 2π .
- replaces particles with standing waves (wavefunctions), where n is number of
waves in the orbit (see figure below).
Equations in the Bohr model
Angular Momentum:
L = n h /2π = m v r
Centripetal Force:
Fcp = mv2 / r = k Z e (e / r2)
Total Energy:
E = ½ mv2 - k Z e2 / r
These three equations can be used to find the orbital radii and energy level per principle quantum
number (n)
r(n) = n2 [ h2 / 4π2 m e2 k Z]
E(n) = - [ 2π2 m e4 k2 Z2 / h2 ] / n2
For the ground state of hydrogen, n = 1;
r(n=1) = 0.0529 nm = ao (the Bohr radius)
E(n=1) = -13.6 eV
ΔE = E(m) – E(n) = hc / λ
where this is the wavelength of light emitted
when the electron transitions between
energy levels, and not the wavefunction of
the orbit of the electron (see above).